We present the results of an optical search for ionized gaseous nebula
e surrounding luminous, ''supersoft'' X-ray sources in the Large and S
mall Magellanic Clouds. This relatively new and mysterious X-ray class
has characteristic luminosities similar to 10(37)-10(38) ergs s(-1) w
ith effective temperatures in the range of 2-6 x 10(5) K. The presence
of a large flux of UV and soft X-ray photons from these objects has l
ed to predictions of bright optical emission lines from the local inte
rstellar medium. One such object, CAL 83 in the LMC, was known to have
an associated nebula, and we quantify here the asymmetry and luminosi
ty of this remarkable nebula. Deep images were made using narrowband f
ilters to isolate the emission lines of H alpha and [O III] (gamma 500
7). In these emission lines, the nebula is detected out to distances a
s far as 25 pc from the central object, and the integrated luminosity
in each line is of order similar to 100 L.. Model calculations of such
nebulae for chemical abundances characteristic of the LMC indicate th
at similar to 1% of the X-ray luminosity of the central source is repr
ocessed into the nebular H alpha and [O III] gamma 5007 emission lines
, from which we conclude that the time-averaged X-ray luminosity of th
e central source, CAL 83, is greater than 3 x 10(37) ergs s(-1). The b
right inner nebula contains similar to 150 M. within 7.5 pc of CAL 83,
which clearly indicates that the nebular material has its origin in t
he interstellar medium. In sharp contrast, there were null detections
for nebulae associated with nine other luminous, supersoft X-ray sourc
es in the LMC and SMC, with upper limits for the [O III] luminosity th
at are a factor of similar to 10 below that for CAL 83. For eight of t
hese latter sources, we conclude that either their time-averaged lumin
osity is substantially below that of CAL 83, or that the local interst
ellar medium is much less dense. The latter effect may be enhanced by
expansion of the ionized nebula during the last several million years.